Abstract: The study of modelling and scheduling problem in real-time system is research focus of operations research and control theory.  This paper studies a scheduling algorithm of single-processor in real-time system, especially Rate Monotonic (RM) and Earliest Deadline First (EDF), and show that RM is a typical static scheduling algorithm and EDF is a typical dynamic scheduling algorithm.  Moreover, the paper prove that RM is the best in static priority scheduling algorithm of single-processor and EDF is the best dynamic priority one's.  At last, in order to make the modelling and scheduling better for real-time system, a new abstracting means of task processing action is put forward: Time and Local remaining Execution-Time plane (T-LET plane).  Based on this method, the paper set up single-processor flow model and BLREF scheduling algorithm, and point out their background of geometry.

Key words: real-time system, single-processor, static scheduling algorithm, dynamic scheduling algorithm